Question: Two numbers have a difference of 3 and a sum of 31. What is the larger of the two numbers?
Answer: Let the numbers be $x$ and $y$.  We have $x+y=31$ and $x-y=3$.  Summing these equations, we get $2x=34$, or $x=17$.  Since $x-y$ is positive, this is the larger number, so the answer is $\boxed{17}$.